Length-Preserving Directions and Some Diophantine Equations
Number Theory
2021-06-24 v1 Spectral Theory
Abstract
We study directions along which the norms of vectors are preserved under a linear map. In particular, we find families of matrices for which these directions are determined by integer vectors. We consider the two-dimensional case in detail, and also discuss the extension to the three-dimensional case.
Keywords
Cite
@article{arxiv.2106.12019,
title = {Length-Preserving Directions and Some Diophantine Equations},
author = {Juan Tolosa},
journal= {arXiv preprint arXiv:2106.12019},
year = {2021}
}
Comments
5 figures